Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20254588 | C2 | semidirect |
| 2. #20253488 | C2 | semidirect |
| 4. #20242022 | C2 | semidirect |
| 5. #20241862 | C2 | semidirect |
| 6. #20241728 | C2 | semidirect |
| 7. C47×#1287 | C2 | semidirect |
| 196. #1287 | D47 | semidirect |
| 228. C47 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254588 | 2 |
| #20253488 | 2 |
| #20253389 | 2 |
| #20242022 | 2 |
| #20241862 | 2 |
| #20241728 | 2 |
| C47×#1287 | 2 |
| #10042 | 47 |